Vertices not selectable
You have a subdivision surface modifier enabled. These modifiers are helpful since they are procedural, meaning that you can easily undo, clear, or modify what came before them.

Subdivision surface is helpful since it allows you to get smoother, and higher resolution meshes (the solid mesh shown below) from a lower resolution source mesh (the transparent wireframe mesh). That lower resolution source mesh also makes it easier to make edits, though there are some cases where that isn't helpful and you have to apply the subsurf modifier.

If you don't want to view the subdivide surface modifier while in edit mode, you can disable the button shown in the screenshot below. If you need direct access to specific vertices, edges or faces that were created by the subsurf modifier, apply the modifier. Keep in mind that if you apply the modifier, you won't be able to undo that step once you go beyond the max undo steps.